I've heard of the 6HLS and can confirm that it is indeed a 6mm wildcat based on the .250 Savage case. I've never seen one so that's all I can add. You could form brass by necking up 22-250 brass which would make it a little easier to find "starter brass" than .250 Savage.
Probably was brewed up by a guy in search of the "magic" cartridge case size for the bore...not overbore or underbore...getting the most efficient use of the powder needed to get the velocity they're in search of, minimizing the recoil for their velocity goal, etc...
I know quite a few people consider the .243 and 6mm/.244Rem a bit overbore and I believe this is what lead to the slightly smaller 6mm cartridges like the 6mmBR, 6mm International, etc. BTW, the 6mm International is another wildcat based on the .250 Savage case necked to 6mm.
And as Kirk said...it was maybe originally brewed up by a guy who had too much .250 Savage brass laying around and an overstock of 6mm bullets.
Have you tried checking for the 6HLS in Cartridges of the World by Frank Barnes?